Three-manifold

Tags: #todo #subjects/geomtop #three-manifolds

Three-manifold

Take a look at Machlachlan and Reid’s book “The Arithmetic of Hyperbolic 3-Manifolds”. #resources

Since finite volume hyperbolic structures are unique whenever an \(n\)-manifold (\(n\geq 3\)) has them, any invariants of the hyperbolic structure are invariants of the manifold. Hyperbolic manifolds are \(K(\pi,1)\) spaces, so they’re not just diffeo/homeomorphism invariants, but invariants of the homotopy-type.

  • Rohklin invariant : a \({\mathbb{Z}}/2\) invariant \(r\) for \(\mathbb{Z}\operatorname{HS}^3\)
  • Casson invariant : a \({\mathbb{Z}}\) invariant \(c\) for \(\mathbb{Z}\operatorname{HS}^3\) where \(c\operatorname{mod}2 = r\).
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#todo #subjects/geomtop #three-manifolds #resources